A metre is $39.37079$ inches, shew by the theory of continued fractions that $32$ metres is nearly equal to $35 y a r d s$ .

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Solution

To show that $32$ metres is nearly equal to $35$ yards

As we know,

$1 m e t r e = 39.37079 \times \frac{1}{36}$ yards
$= 1.0936$ yards

Also,
$1.0936 = 1 + \frac{1}{10 +} \frac{1}{1 +} \frac{1}{2 +} \frac{1}{6 +} \frac{1}{6}$

$∴$ The convergents are

$1, \frac{11}{10}, \frac{12}{11}, \frac{35}{32}, . . . . .$

Thus, $32$ metres nearly equal to 35 yards.

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Question 133

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A metre is 39.37079 inches, shew by the theory of continued fractions that 32 metres is nearly equal to 35 yards.

To show that 32 metres is nearly equal to 35 yards As we know,1metre=39.37079×136 yards =1.0936 yards Also, 1.0936=1+110+11+12+16+16 ∴ The convergents are 1,1110,1211,3532,..... Thus, 32 metres nearly equal to 35 yards.

A metre is $39.37079$ inches, shew by the theory of continued fractions that $32$ metres is nearly equal to $35 y a r d s$ .